Earth, Sun and Vega.

Hello,
I'm trying to calculate something and I wonder if someone can
help me.
The Earth travels around the Sun and the Sun is travelling towards
Vega (not quite, so I'm told?). I'd like to know at what moment (which
day in the solar year) the Earth is moving in the same direction as
the Sun, towards Vega. Also, as the Earth's mouvement is not in the
same plane as that of the Sun, what is the angle(a) between these two
planes.
What I want to find out is the Earth's maximum absolute speed. This
would be 30km/s (the Earth's speed around the Sun) plus 20km/s (the
Sun's speed towards Vega) multiplied by cos(a). But these two speeds
only add up at a precise time of year, which I haven't managed to work
out.
Hoping to hear from you. Regards, Ken